The Pentagon said Wednesday it has suspended its efforts to recoup re-enlistment bonuses and incentive payments from service members and war veterans who received them erroneously, outlining a series of steps to quell a growing outcry.

U.S. Secretary of Defense Ash Carter vowed Tuesday to resolve a burgeoning controversy over Pentagon efforts to claw back millions of dollars in re-enlistment bonuses from current and former California National Guard soldiers, many of whom served...